Contribution and solvency risk in a defined benefit pension scheme

This paper presents a stochastic investment model for a defined benefit pen sion scheme, in the presence of no real rates of return. The spread method of adjustment to the normal cost is used to deal with surpluses or deficien cies. Two types of risk are identified, the "contribution rate risk" and th e "solvency risk" which are concerned with the stability of the contributio ns and the security of the pension fund, respectively. A performance criter ion is introduced to deal with the simultaneous minimisation of these two r isks, using the fraction of the unfunded liability paid off (k) or the spre ad period (M) as the control variable. A full numerical investigation of th e optimal values of k and M is provided. The results lead to practical conc lusions about the optimal funding strategy and, hence, about the optimal ch oice of the contribution rate subject to the constraints needed for the con vergence of the performance criterion. (C) 2000 Elsevier Science B.V. All r ights reserved. JEL classification: C61.